Question

The square pyramid has a volume of 768 cubic inches. The height equals 1/6x and the base is just x. What is the value of x ?

Answer 1

The volume for a pyramid is $V= \frac{1}{3} Bh$, where B is the area of the base and h is the height.  We are given the volume, and the base and height in terms of x.  Our formula then looks like this: $768= \frac{1}{3} (x)( \frac{1}{6} x)$.  Simplifying the right side we have $768= \frac{1}{18} x^{2}$.  Multiply both sides by 18 to get rid of the fraction and we have $13824= x^{2}$, so x = 117.575